Journal
STUDIES IN APPLIED MATHEMATICS
Volume 148, Issue 4, Pages 1703-1721Publisher
WILEY
DOI: 10.1111/sapm.12488
Keywords
Cauchy matrix approach; integrable system; self-dual Yang-Mills equation; solution
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Funding
- Science and Technology Commission of Shanghai Municipality
- National Natural Science Foundation of China
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The Cauchy matrix approach is introduced to solve the SU(2) self-dual Yang-Mills equation. New relations are derived from a Sylvester matrix equation coupled with certain dispersion relations, leading to a broad class of explicit solutions of the equation under Yang's formulation.
The Cauchy matrix approach is developed to solve the SU(2)$\mathbf {SU}(2)$ self-dual Yang-Mills (SDYM) equation. Starting from a Sylvester matrix equation coupled with certain dispersion relations for an infinite number of coordinates, we derive some new relations that give rise to the SDYM equation under Yang's formulation. By imposing further constraints on complex independent variables, a broad class of explicit solutions of the equation under Yang's formulation are obtained.
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